Find the coordinates of the vertex of the following parabola algebraically.
Write your answer as an (x, y) point.
y = x2

Answer:

[tex]m\angle C=20^{\circ}\\m\angle B = 127^{\circ}\\b=37\\[/tex]

Step-by-step explanation:

The Law of Sines for any triangle is:

[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]

Let's solve for [tex]m\angle C[/tex] first:

[tex]\frac{\sin33^{\circ}}{25}=\frac{\sin (m\angle C)}{16},\\\sin (m\angle C)=\frac{16\cdot \sin33^{\circ}}{25}, \\m\angle C= \sin^{-1}(\frac{16\cdot \sin33^{\circ}}{25})\approx \fbox{$20^{\circ}$}[/tex]

Since the sum of the interior angles in a triangle is always [tex]180^{\circ}[/tex], the measure of angle B is [tex]m\angle B=180-33-20=\fbox{$127^{\circ}$}[/tex].

Now we can use to solve for side length [tex]b[/tex]:

[tex]\frac{\sin33^{\circ}}{25}=\frac{\sin 127^{\circ}}{b},\\b=\frac{25\cdot \sin127^{\circ}}{\sin33^{\circ}}\approx \fbox{37}[/tex].

Answer: Exactly what I said!

Step-by-step explanation:

320 + 120 = 440

Not 100!

If it was 220 - 120, it would be 100!

Thanks for the free points by the way! :3

Answer:

y = x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 1, thus

y = x + c ← is the partial equation

To find c substitute (- 3, 4) into the partial equation

4 = - 3 + c ⇒ c = 4 + 3 = 7

y = x + 7 ← equation of line

Hope this helps.

Answer:

C = 2π22 = 138.230076

138.230076 X 11 = 1520.53084

π22^2 = 1520.53084

1520.53084 + 1520.53084 = 3041.06168

3041.0 cm squared

divide by 100 = 30.41

30.41 X 0.2 = 6.082

$6.08

he must take less expensive

Answer:

B choice

Step-by-step explanation:

[tex]y = mx + b[/tex]

where m = slope and b = y-intercept.

The value of m is 3/4. That means slope is 3/4. Changing 3/4 to - 3/4 will make the slope become negative. Therefore the answer is B.

Answer: b) the slope of the line will change from positive to negative

Answer:

B

Step-by-step explanation:

Answer:

B. (2+5) + 7 = 2 + (5+7)

Step-by-step explanation:

The Associative Property of Addition states that:

(a+b) + c = a + (b+c).

Or, any three or more numbers added together will have the same sum no matter how they are grouped.

Answer choice B is the only choice that exhibits this, and so, B is the answer.

Hope this helps!

Answer:

126 km/h

378 km

Step-by-step explanation:

To convert m/s into km/h, we multiply it by 3.6.

35 m/s x 3.6 = 126 km/h.

Distance travelled in 3 hours = 126 x 3 km = 378 km.

Answer:

it should be B, sorry if im wrong! :(

Step-by-step explanation:

Answer:

(-2, 0, 1, 3)

Step-by-step explanation:

From the given graph, there are four x-intercepts, which are the points the graph crosses the x-axis

Taking the y-axis as the given vertical line, and each demarcation as representing one unit division, we have;

The x coordinates of the x-intercepts are given as follows;

1) Two lines to the left of the origin which represents "-2"

2) Through the origin, which represents "0"

3) One line to the right of the origin which represents "1"

4) Three lines to the right of the origin which represents "3"

The set of values that represents the x-intercepts of the function are;

(-2, 0, 1, and 3)

Step-by-step explanation:

2x-(2x-1)-1=0

2x-2x+1-1=0

0=0

I think,this system has no solution

Answer:

The answer is 44! The answer is 44!

Step-by-step explanation:

The answer is 44!

9514 1404 393

Answer:

  f(g(x)) = 50x² +140x +93

Step-by-step explanation:

Put the function argument in place of x and simplify.

  f(g(x)) = f(5x+7) = 2(5x+7)² -5

  = 2(25x² +70x +49) -5

  f(g(x)) = 50x² +140x +93

_____

We took advantage of the knowledge that ...

  (a + b)² = a² +2ab +b² . . . . . where a=5x and b=7

Answer:

720 beans in total

Step-by-step explanation:

I would set this up with proportions, so-

1             180

4             x

Then cross multiply-

4 x 180 = 720

Divide-

720/1 = 720

720 is your answer

Answer:

UY = 14

Step-by-step explanation:

In the given figure

∵ TUV is a triangle

∵ UZ, VX, and TW are medians

∵ UZ ∩ VX ∩ TW at point Y

∴ Y is the point of intersection of the 3 medians

→ By using the 2nd rule above

∵ The point Y divide UZ at the ratio of 2: 1 from the vertex U

∴ UY: YZ = 2: 1

∴ [tex]\frac{UY}{YZ}[/tex] = [tex]\frac{2}{1}[/tex]

→ By using cross multiplication

∵ UY × 1 = YZ × 2

∴ UY = 2YZ

∵ UZ = UY + YZ

∴ UZ = 2 + 1 = 3 parts

∵ UY = 2 parts

∴ [tex]\frac{UY}{UZ}[/tex] = [tex]\frac{2}{3}[/tex]

→ Multiply both sides by UZ

∴ UY =  [tex]\frac{2}{3}[/tex] UZ

∵ UZ = 21

∴ UY =  [tex]\frac{2}{3}[/tex] (21)

∴ UY = 14

Answer:

28 inches long

Step-by-step explanation:

just multiply 7 and 4

Answer:

7200

Step-by-step explanation:

Find the exponents first.

10^3 = 1000

10^2 = 100

So..

7 x 1000 + 2 x 100

Do the multiplication first (BEDMAS - Brackets Exponents Division Multiplication Addition Subtraction).

7000 + 200 = 7200

answer:

8x - 16 + 5x + 15 = 90

and

8x - 6 + 18x + 4 = 180

Answer:

293,163

Step-by-step explanation:

300,000-7,000+100+60+3

Answer:

5

Step-by-step explanation:

You have to add the boxes between j and k and that’s how u get your length

Answer:

11:35 AM

Step-by-step explanation:

Lets start with the hours:

9+2=11

Now the minutes:

15+20=35

Now put them together:

11:35 AM

Answer:

11:35

Step-by-step explanation:

9 plus 2 equals 11

20+15 equals 35

9514 1404 393

Answer:

   -135/14

Step-by-step explanation:

There are an infinite number of rational numbers between any pair of numbers you name. These two number have the decimal values ...

  -67/7 = -9 4/7 = -9.571428... (repeating)

  -78/8 = -9 3/4 = -9.75

So, numbers like -9.6 = -48/5, or -9.7 = -97/10 are rational numbers that lie in the range you specified.

If you like, you can convert these numbers to ones with a common denominator (56).

 -67/7 = -536/56

 -78/8 = -546/56

These limits suggest several possible rational numbers with 56 as a denominator: -540/56 = -135/14, for example.

Answer:

A scale factor of 4in to 5in should be used

Step-by-step explanation:

Given

[tex]Original\ Measurement = 4.5\ in[/tex]

[tex]Scale\ Measurement = 3.6\ in[/tex]

Required

Determine the scale to use

The scale to use can be represented as:

[tex]Scale = Scale\ Measurement : Original\ Measurement[/tex]

This gives:

[tex]Scale = 3.6\ in : 4.5\ in[/tex]

Divide by 0.9

[tex]Scale = \frac{3.6}{0.9}\ in : \frac{4.5}{0..9}\ in[/tex]

[tex]Scale = \frac{3.6}{0.9} : \frac{4.5}{0.9}[/tex]

[tex]Scale = 4 : 5[/tex]

Answer:

Here is the summary of true statements:

A) The statement of the function modeled is (0, 3) is TRUE.

D) the equation for the line function is y = 2x+3 is TRUE.

E) the given table represents the linear function is TRUE

Step-by-step explanation:

Given the table

x   1      3      5      7

y   5      9      13     17

E)

It is clear that there is a CONSTANT CHANGE in the x and y values of the graph.

THE CONSTANT CHANGE IN X VALUES

i.e. 3-1=2, 5-3=2, 7-5=2

THE CONSTANT CHANGE IN Y VALUES

i.e. 9-5 = 4, 13 - 9 = 4, 17 - 13 = 4

Thus, the given table represents the linear function is TRUE

B)

It is clear that the value of y increase as the value of x increases.

Thus, the statement ''the value of y decreases as the value of x increases'' is FALSE!

D)

We know that the slop-intercept form of the line equation is

[tex]y = mx+b[/tex]

where m is the slope and b is the y-intercept.

Determining the equation

Taking two points

(1, 5)

(3, 9)

Finding the slope between (1, 5) and (3, 9)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [9 - 5] / [3 - 1]

               = 4 / 2  

               = 2

Thus, the slope of the line = m = 2

now substituting m = 2 and the point (1, 5) to determine the y-intercept

y = mx+b

5 = 2(1) + b

b = 5-2

b = 3

Thus, the value of y-intercept b = 3

substituting b = 3 and m = 2 in the slope-intercept form

y = mx+b

y = 2x+3

Therefore, the equation for the line function is y = 2x+3 is TRUE

A)

We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

We already know that the y-intercept b = 3

It means the y-intercept modeled is (0, 3)

Therefore, the statement of the function modeled is (0, 3) is TRUE.

C)

We have already got the equation

y = 2x+3

substituting x = 8

y = 2(8)+3

y = 10+3

y = 13

so at x = 8, the value of y = 13

Therefore, the statement that the ''On a graph of the function when x = 8, the value of y will be 2'' is FALSE!

Conclusion:

Here is the summary of true statements:

A) The statement of the function modeled is (0, 3) is TRUE.

D) the equation for the line function is y = 2x+3 is TRUE.

E) the given table represents the linear function is TRUE

Answer:

AAS only

Step-by-step explanation:

vertical angle

Answer:

The answer is A.

the angles are opposite angles, therefore they have the same value. they're equal to each other. you set them equal to each other to find the value of x.

Step-by-step explanation:

i hope this helps :)

Answer:

I think answer is

b. (2,1)

:-)

Answer:

minimum

Step-by-step explanation:

this is a minimum since the vertex is at the bottom

it would be a max if the vertex is at the top and the graph opens down